You're eighteen, fresh out of school, and you've found a job. It doesn't pay much, but you feel pretty lucky at a time when unemployment among your peers is at record levels. Then you start looking for a flatshare within a bus or bike ride of your workplace and it all comes unstuck.

If you accept the government's standard definition of affordability, then this young person earning the minimum wage (£4.98 an hour for 18- to 20-year-olds) couldn't afford afford to rent a room in the average shared flat in any of 33 local authorities in London, with four approaching affordability: Barking & Dagenham, Bexley, Havering, and Richmond upon Thames.

In every borough the median rent would swallow up more than 35% of take-home pay, making the rent unaffordable by the standard definition. This isn't a central London, prime market problem; average rents are shockingly high across the capital.

London rent map.

Try getting to your new job in Hammersmith from Bexley every day without racking up a huge Oyster card bill. Too often the costs escalate further as short-term tenancies end, forcing people to go on another laborious flat search, pay rising agents' fees and accept another rent increase in a spiralling market.

An adult on the minimum wage wouldn't be able to afford the median two bed flat in any borough; the idea of one parent bringing home enough bread for a family is a nonsense.

Of course these are median rents across entire boroughs. There will be cheaper streets, and homes with below-average rents. But if we value mixed communities and choice, I think these averages tell an important story about the state of our rental market.

I have published an interactive map that helps people understand just how difficult it is to pay the rent in London, especially if you earn a low wage. So much of the public debate seems premised on the idea that you shouldn't need benefits if you have a job, but the rising number of housing benefit claimants in work tell another story.

This government and the mayor of London have become dangerously detached from the realities of life for young Londoners. David Cameron's appalling suggestion that housing benefit should be withdrawn altogether from young people is just the latest attack on our young based on half-baked populism.

The housing benefit bill in London isn't so high because a wave of feckless youngsters shirking work. It's because there are so few jobs – and too few that do exist pay enough to cover the rent. High rents are one of the defining barriers to prosperity, ambition and social mobility for young people.

I also published the maps to gather views on that standard definition of affordability: 35% of take-home pay. A lot of people have told me that they've always paid at least 50% of income – often more – towards their rent. The definition seems completely detached from the experiences of the young people who have responded to my survey, and from actual rent levels across London.

If we really think the "35% of take-home pay" definition is correct, then London mayor Boris Johnson needs to develop and lobby for the sorts of radical policies that will bring rents back in line with that goal. Just treading water on affordable house building and accrediting the better landlords won't be enough.